A circle has a radius of ${9}$. An arc in this circle has a central angle of $120^\circ$. What is the length of the arc? Either enter an exact answer in terms of $\pi$ or use $3.14$ for $\pi$ and enter your answer as a decimal. ${120^\circ}$ ${9}$
Answer: First, calculate the circumference of the circle. ${120^\circ}$ ${9}$ ${18\pi}$ ${c} = 2\pi r = 2\pi ({9}) = {18\pi}$ The ratio between the arc's central angle ${\theta}$ and $360^\circ$ is equal to the ratio between the arc length ${s}$ and the circle's circumference ${c}$. $\dfrac{{\theta}}{360^\circ} = \dfrac{{s}}{{c}}$ $\dfrac{{120}^\circ}{360^\circ} = \dfrac{{s}}{{{18\pi}}}$ $\dfrac{1}{3} = \dfrac{{s}}{{18\pi}}$ $\dfrac{1}{3} \times {18\pi} = {s}$ $6\pi = {s}$ ${120^\circ}$ ${9}$ ${18\pi}$ ${6\pi}$